Problem Solving

An airlines passenger is planning a trip that involves three connecting flights that leave from Airports A, B and C, respectively. The first flight leaves Airport A every hour, beginiing at 8:00 a.m and arrives at Airport B 2 1/2 hours later. The second flight leaves Airport B every 20 minutes, beginning at 8:00 a.m, and arrives at Airport C 1 1/6 hours later. The third flight leaves Airport C every hour, beginning at 8:45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep in their schedules?

(A) 25 min
(B) 1 hr 5 min
(C) 1 hr 15 min
(D) 2 hr 20 min
(E) 3 hr 40 min

answ-B

Assume he catches the flight from A at 8:00 a.m, so he reaches B at (10.30 a.m) - 2 1/2 hr travel.

List out departing times of flights at B.

8:00
8:20
|
|
10:00
10:20
10:40 - (this would be the earliest he can catch) (wait for 10 mins)

So he leaves B at 10:40 and reaches C at (11:50 a.m) - 1 1/6 hrs travel.

Now C has flights leaving every hour from 8:45

8:45
11:45
12:45 - (this will be the earliest flight he can catch) (wait for 55 mins)

Total waiting time = 55+10 = 65 mins B

I could envision a problem like this in which the passenger, in optimizing for minimal lay over time, would be required to take a later flight. Would anyone out there be aware of any optimization formulas that could be applied to a problem like this.